# Snub cube

Snub cube Click on picture for large version. Click on picture for large version.
TypeArchimedean
Faces32 triangles
6 squares
Edges60
Vertices24
Vertex configuration3,3,3,3,4
Symmetry groupoctahedral (O)
Dual polyhedronpentagonal icositetrahedron
Propertiesconvex, semi-regular (vertex-uniform), chiral

The snub cube, or snub cuboctahedron, is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a cube or an octahedron.

Missing image
Snub_cube_flat.png
image:Snub cube flat.png

The snub cube has 38 faces, of which 6 are squares and the other 32 are equilateral triangles. It has 60 edges and 24 vertices. In three-dimensional space, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In higher-dimensional spaces, these are congruent.

Canonical coordinates for a snub cube are all the even permutations of (±1, ±ξ, ±1/ξ) with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where ξ is the real solution to ξ32+ξ=1, which can be written

[itex]\xi = \frac{1}{3}\left(\sqrt{17+\sqrt{297}} - \sqrt{-17+\sqrt{297}} - 1\right)[itex]

or approximately 0.543689. Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs gives a different snub cube, the mirror image.

The snub cube should not be confused with the truncated cube.

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